论文信息 - Linear sections of GL(4; 2)

Linear sections of GL(4; 2)

For V = V (n;q); a linear section of GL(V )=G L(n;q) is a vector subspace S of the n 2 -dimensional vector space End(V ) which is contained in GL(V )[ f0g: We pose the problem, for given (n;q); of classifying the dierent kinds of maximal linear sections of GL(n;q): IfS is any linear section of GL(n;q) then dimSn: The case of GL(4; 2) is examined fully. Up to a suitable notion of equivalence there are just two classes of 3-dimensional maximal normalized linear sections M3;M 0, and three classesM4;M 0;M 00 of 4-dimensional sections. The subgroups of GL(4; 2) generated by representatives of these ve classes are respectivelyG3 = A7; G 0

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